Electrical Engineering and Control Systems / MISCIT 2nd year

 Optimization and Optimal Control (21 h + 15 h labs)

Multivariable robust control (20 h + 16 h labs)

Visit the full page about this course

Feedback control design, diagnostic/supervision and process optimization typically require a specific modeling approach, which aims to capture the essential dynamics of the system while being computationally efficient. The first part of the class details the guiding principles that can be inferred from different physical domains and how multi-physics models can be obtained for complex dynamical systems while satisfying the principle of energy conservation. This leads to algebro-differential mathematical models that need to be computed with stability and computational efficiency constraints. System identification constitutes the second part of the class, to include knowledge inferred from experimental data in the input/output map set by the model. It provides methods to evaluate the model performance, to estimate parameters, to design "sufficiently informative" experiments and to build recursive algorithms for online estimation.

Visit the full page about this course

The Adaptive Control course covers fundamental concepts and practical techniques to achieve or maintain a desired level of performance in a control system, especially when the parameters of the plant model are unknown or change over time.

Outline :

1. Introduction to the adaptive control

Basic Adaptive Control Configurations, Application examples.

2. Parameter adaptation algorithms

Gradient algorithm, recursive least squares Algorithm, stability of parameter adaptation algorithms.

3. Identification in open loop – a brief review

Data acquisition, model complexity, parameter estimation, model validation.

4. Iterative identification in closed loop and controller redesign

Algorithms for identification in closed loop (CLOE, F-CLOE and AF-CLOE), Validation of models identified in closed loop, Iterative identification in closed loop and controller re-design.

5. Direct and Indirect Adaptive Control

Tracking and regulation with independent objectives (known parameters), adaptive tracking and regulation with independent objectives (direct adaptive control), pole placement (known parameters), adaptive pole placement (indirect adaptive control).

Lab :

Iterative identification and controller re-design for the Throttle Valve.

Visit the full page about this course

Embedded control & Labview (18 h)

• Become comfortable with the LabVIEW environment and data flow execution.
• LabVIEW Concepts: 
  • Acquiring, saving and loading data; 
  • Find and use math and complex analysis functions; 
  • Work with data types, such as arrays and clusters; 
  • Displaying and printing results. 
• Understand the principle of Embedded systems. 
• Be able to use Labview and the RT and FPGA Modules specially with Embedded systems. 
• Understand data exchanges between several systems.

Modeling labs (27 h)

Feedback control design, diagnostic/supervision and process optimization typically require a specific modeling approach, which aims to capture the essential dynamics of the system while being computationally efficient. The first part of the class details the guiding principles that can be inferred from different physical domains and how multi-physics models can be obtained for complex dynamical systems while satisfying the principle of energy conservation. This leads to algebro-differential mathematical models that need to be computed with stability and computational efficiency constraints. System identification constitutes the second part of the class, to include knowledge inferred from experimental data in the input/output map set by the model. It provides methods to evaluate the model performance, to estimate parameters, to design "sufficiently informative" experiments and to build recursive algorithms for online estimation.

Visit the full page about this course

Safety, supervision and diagnosis of industrial plants 

The objective of this class is to introduce the concept of fault detection and fault diagnosis for complex systems and to present different classes of methods which have proven their performances in practical applications. 

Visit the full page about this course

Security of Network and Applications (18h + 8h labs)

The objective of this class is to introduce security principles, on the theoretical, organizational and technical aspects. The points which are more specifically developed are: detection errors, firewall technics, network architecture, cryptology and VPN, anti-virus strategy. Are also discussed how to implement a security strategy, and some elements for the definition of a security policy. Some elements about safe networks, or networks for safety or critical applications, are also studied.

Field buses and Zigbee (10.5 h + 15h labs)

Distributed Algorithms and Network Systems (13.5 h + 6h labs)

Objectives Distributed algorithms aim at obtaining a global goal by exploiting a large number of simple devices (``agents''), and their local interactions. These algorithms can be for the purposes of estimation in a wireless sensor network, or control e.g. of a self-organized robotic fleet. This introductory class will first review the necessary tools from graph theory and Markov chains, and then present consensus: a prototypical example of distributed algorithm, as well as a building block for more complex algorithms. Theory will be accompanied by implementation on a real-world sensor network: FIT/IoT LAB.Class schedule 

1. Introduction: network systems 
2. Graphs: fundamentals of algebraic graph theory
3. Markov chains: convergence to invariant measure, Perron-Frobenius theorem 
4. Consensus (time-invariant graph) 
5. Consensus (gossip: randomly varying graph) 
6. Consensus-based algorithms: using consensus as a building block of other algorithms (e.g., localisation from relative measurements, least-squares regression, gradient descent minimization, distributed Kalman filter, counting nodes in an anonymous network) 
7. Labs (3): implementation of distributed algorithms on real sensor network, remotely using FIT/IoT LAB. Programming language: C.

Visit the full page about this course

Under Floor Air Distribution for Intelligent Buildings

This new technology presents many advantages in comparison with traditional ventilation systems, such as energy consumption reduction, comfort and health. UFAD efficiency directly depends on distributed sensing capabilities (thanks to the deployment of a wireless sensor network) and on an appropriate multivariable feedback control design. The idea comes then to conceive a prototype in order to validate theoric and simulation results and to implement control algorithms. The prototype represents a ventilated floor composed of three interconnected levels: under floor, four rooms and upper floor. The related IPA projects are dedicated to air conditioning operation, with an emphasis on the modeling and control of airflow in each level and between the adjacent rooms. 

Controlling instability: the inverted half cube 

Unstable processes are typically not controllable with open-loop strategies and hence provide valuable benchmarks for feedback control applications. Addressing the stabilization of such processes implies a specific care of the key control design issues, such as performance limitations, communication and computation constraints, robustness, nonlinearities etc. 
The inverted half cube, designed and built by IPA students, implies to stabilize the half cube on its lower edge thanks to a cart driven with a LEGO NXT module. This novel version of the classical "inverted pendulum" implies to solve the same control problems as those associated with walking biped robots, a missile propelled by a jet reaction, a load suspended from a crane, etc...

Visit the full page about this course

Visit the full page about this course

Visit the full page about this course

 Optimization and Optimal Control (21 h + 15 h labs)

Multivariable robust control (20 h + 16 h labs)

Visit the full page about this course

Feedback control design, diagnostic/supervision and process optimization typically require a specific modeling approach, which aims to capture the essential dynamics of the system while being computationally efficient. The first part of the class details the guiding principles that can be inferred from different physical domains and how multi-physics models can be obtained for complex dynamical systems while satisfying the principle of energy conservation. This leads to algebro-differential mathematical models that need to be computed with stability and computational efficiency constraints. System identification constitutes the second part of the class, to include knowledge inferred from experimental data in the input/output map set by the model. It provides methods to evaluate the model performance, to estimate parameters, to design "sufficiently informative" experiments and to build recursive algorithms for online estimation.

Visit the full page about this course

The Adaptive Control course covers fundamental concepts and practical techniques to achieve or maintain a desired level of performance in a control system, especially when the parameters of the plant model are unknown or change over time.

Outline :

1. Introduction to the adaptive control

Basic Adaptive Control Configurations, Application examples.

2. Parameter adaptation algorithms

Gradient algorithm, recursive least squares Algorithm, stability of parameter adaptation algorithms.

3. Identification in open loop – a brief review

Data acquisition, model complexity, parameter estimation, model validation.

4. Iterative identification in closed loop and controller redesign

Algorithms for identification in closed loop (CLOE, F-CLOE and AF-CLOE), Validation of models identified in closed loop, Iterative identification in closed loop and controller re-design.

5. Direct and Indirect Adaptive Control

Tracking and regulation with independent objectives (known parameters), adaptive tracking and regulation with independent objectives (direct adaptive control), pole placement (known parameters), adaptive pole placement (indirect adaptive control).

Lab :

Iterative identification and controller re-design for the Throttle Valve.

Visit the full page about this course

Non linear control (20 h)

1. Introduction to nonlinear systems: representation and specific features 
2. Nonlinear systems analysis: stability, tangent linearization, Lyapunov methods 
3. State feedback control of nonlinear systems: approximate linearization, exact linearization, backstepping, sliding modes 
4. State observers for nonlinear systems: Extended Kalman Filter, Output injection, High gain designs 
5. Observer-controller schemes: adaptive methods, output feedback control 

 Predictive control (14 h)

• Predictive control 
  • Introduction to constraints
  • Finite horizon predictive control
  • Stability conditions
  • Examples
• Predictive control of nonlinear systems
  • Closed loop stability
  • Control parametrization
  • Optimization tools
  • Examples
• Complete case study

List of examples from Mechatronics: Inverted pendulum, tiliting trains, elastic crane, Boeing aircraft, chain of masses linked through springs, automate-manual transmission (AMT), etc.

Prerequisites: State space and transfer approaches for linear systems, optimisation

Visit the full page about this course

Under Floor Air Distribution for Intelligent Buildings

This new technology presents many advantages in comparison with traditional ventilation systems, such as energy consumption reduction, comfort and health. UFAD efficiency directly depends on distributed sensing capabilities (thanks to the deployment of a wireless sensor network) and on an appropriate multivariable feedback control design. The idea comes then to conceive a prototype in order to validate theoric and simulation results and to implement control algorithms. The prototype represents a ventilated floor composed of three interconnected levels: under floor, four rooms and upper floor. The related IPA projects are dedicated to air conditioning operation, with an emphasis on the modeling and control of airflow in each level and between the adjacent rooms. 

Controlling instability: the inverted half cube 

Unstable processes are typically not controllable with open-loop strategies and hence provide valuable benchmarks for feedback control applications. Addressing the stabilization of such processes implies a specific care of the key control design issues, such as performance limitations, communication and computation constraints, robustness, nonlinearities etc. 
The inverted half cube, designed and built by IPA students, implies to stabilize the half cube on its lower edge thanks to a cart driven with a LEGO NXT module. This novel version of the classical "inverted pendulum" implies to solve the same control problems as those associated with walking biped robots, a missile propelled by a jet reaction, a load suspended from a crane, etc...

Visit the full page about this course

The subject of this half-semester course are more advanced methods in convex optimization. It consists of 6 lectures, 2 x 1,5 hours each, and can be seen as continuation of the course “Non-smooth methods in convex optimization”.

This course deals with:

Evaluation : A two-hours written exam (E1) in December. For those who do not pass there will be another two-hours exam (E2) in session 2 in spring.

• Topic 1: convex analysis

• Topic 2: convex programming

• Basic notions: vector space, affine space, metric, topology, symmetry groups, linear and affine hulls, interior and closure, boundary, relative interior

• Convex sets: definition, invariance properties, polyhedral sets and polytopes, simplices, convex hull, inner and outer description, algebraic properties, separation, supporting hyperplanes, extreme and exposed points, recession cone, Carathéodory number, convex cones, conic hull

• Convex functions: level sets, support functions, sub-gradients, quasi-convex functions, self-concordant functions

• Duality: dual vector space, conic duality, polar set, Legendre transform

• Optimization problems: classification, convex programs, constraints, objective, feasibility, optimality, boundedness, duality

• Linear programming: Farkas lemma, alternative, duality, simplex method

• Algorithms: 1-dimensional minimization, Ellipsoid method, gradient descent methods, 2nd order methods

• Conic programming: barriers, Hessian metric, duality, interior-point methods, universal barriers, homogeneous cones, symmetric cones, semi-definite programming

• Relaxations: rank 1 relaxations for quadratically constrained quadratic programs, Nesterovs π/2 theorem, S-lemma, Dines theorem Polynomial optimization: matrix-valued polynomials in one variable, Toeplitz and Hankel matrices, moments, SOS relaxations

Visit the full page about this course

This set of courses proposes an overview of recent techniques for the identification, observation, simulation and control of distributed parameter systems. This class of systems is widely used in physics and considered in many applications (such as in environment dynamics, airflow control, structural mechanics, and adaptive optics) having a large or an infinite number of degrees of freedom. A Partial Differential Equation (PDE) usually models them. Their mathematical study asks for a special care to analyze the dynamics behavior and to describe their control properties. Different aspects of this description are considered in this Teaching Unit, by emphasizing the practical methods allowing for some real applications. 

This Teaching Unit is composed by three different courses:

Analysis and control (13.5 h)

Modeling and Inverse problems (13.5h)

Distributed optimization  (13.5h)

Prerequisites: basic mathematical background, control theory of finite dimensional systems (control and observation theory for linear ODEs, in particular optimal LQ regulation) 

• Schedule 
• Modeling
• Control 
• Optimization 
• Communication networks
• Projects & seminars
• Public speaking 

Visit the full page about this course

Embedded control & Labview (18 h)

• Become comfortable with the LabVIEW environment and data flow execution.
• LabVIEW Concepts: 
  • Acquiring, saving and loading data; 
  • Find and use math and complex analysis functions; 
  • Work with data types, such as arrays and clusters; 
  • Displaying and printing results. 
• Understand the principle of Embedded systems. 
• Be able to use Labview and the RT and FPGA Modules specially with Embedded systems. 
• Understand data exchanges between several systems.

Modeling labs (27 h)

Feedback control design, diagnostic/supervision and process optimization typically require a specific modeling approach, which aims to capture the essential dynamics of the system while being computationally efficient. The first part of the class details the guiding principles that can be inferred from different physical domains and how multi-physics models can be obtained for complex dynamical systems while satisfying the principle of energy conservation. This leads to algebro-differential mathematical models that need to be computed with stability and computational efficiency constraints. System identification constitutes the second part of the class, to include knowledge inferred from experimental data in the input/output map set by the model. It provides methods to evaluate the model performance, to estimate parameters, to design "sufficiently informative" experiments and to build recursive algorithms for online estimation.

Visit the full page about this course

Safety, supervision and diagnosis of industrial plants 

The objective of this class is to introduce the concept of fault detection and fault diagnosis for complex systems and to present different classes of methods which have proven their performances in practical applications. 

Visit the full page about this course

Visit the full page about this course

Visit the full page about this course

Project management (10.5 h)

The objectives of this class are to supply the bases of the project management as well as to present the good practices in industries. The quality management according to the standards ISO and the piloting by process are presented through industrial projects. 

This class contains a method to establish a CV as well as simulations of real recruitment interview.Class schedule 

Industrial seminars (27 h for IPA)

• Semi-active damper design and regulation. B. TALON, SOBEN.
• Model-based design for motor control. V. TALON, Renault.
• Case study on warm compression station for cryogenics. B. BRADU, CERN . 
• Keys and social issues to enter the industrial life. M. PRUNIER, Schneider.
• Consulting for inovation in Information Technologies. D. JACQUET, Protoptim .

Research seminars (15 h for CST)

Each year, MiSCIT and GIPSA-lab invite keynote speakers to give a short class on their research topic. The lectures (typically 15h) are given in the Control Systems Department of GIPSA-lab. They focus on the latest results in a specific topic of control and systems theory, and may include some labs to illustrate specific aspects. The attendance is composed as Master and Ph.D. students, as well as engineers, researchers and professors. A basic knowledge in dynamical systems, linear algebra and control theory is expected.

Linear Matrix Inequalities and Sum-of-Squares Optimization in Systems and Controls Theory: A Practical and Theoretical Overview (2013) 

By Mattew M. Peet, Professor of Aerospace Engineering, Arizona State University (USA)

Abstract: The topic of this course will be the use of LMI methods for optimal control of linear, nonlinear and infinite-dimensional systems. We will start by posing all major finite-dimensional optimal control problems as LMIs. This includes both output and full-state feedback control for both the H_\infty and H_2 (LQG) system norms. We will also give a brief introduction to the popular SDP solver SeDuMi. Next, we will give a background on the use of LMIs for optimization of polynomial variables such as in the Sum-of-Squares framework - including the use of the Matlab toolbox SOSTOOLS. We will discuss several theoretical tools for the optimization of polynomials such as various versions of the Positivstellensatz. Finally, we will discuss how LMIs and polynomial optimization have been use to resolve long-standing problems in analysis of nonlinear systems and systems with delay, and how these results have been extended to synthesize optimal controllers for systems with delay and certain classes of partial-differential equations.

Syllabus:

• Day 1: Convex optimization; Semidefinite programming; Linear state-space systems theory; Optimal H_2 and H_\infty dynamic output-feedback controller synthesis. 
• Day 2: Polynomial optimization, Sum-of-Squares; Polya's lemma; Ideals, Varieties; The Positivstellensatz; Robust controller synthesis 
• Day 3: Nonlinear stability analysis; Analysis and control of linear delayed systems; Analysis and control of linear partial-differential equations; Stability Analysis of nonlinear delayed and partial-differential equations. 

Model Reduction (Approximation) of Large-Scale Systems (2012) 

By Charles Poussot-Vassal, Researcher at Onera - The French Aerospace Lab.

Abstract: In the engineering area (e.g. aerospace, automotive, biology, circuits), dynamical systems are the basic framework used for modelling, controlling and analysing a large variety of systems and phenomena. Due to the increasing use of dedicated computer-based modelling design software, numerical simulation turns to be more and more used to simulate a complex system or phenomenon and shorten both development time and cost. However, the need of an enhanced model accuracy inevitably leads to an increasing number of variables and resources to manage at the price of a high numerical cost. This counterpart is the justification for model reduction (see Figure 1). 
The objective of the lecture is to introduce the model reduction (or approximation) problem, within the linear framework only, and, in an increase complexity, some of the well established and modern techniques to solve this class of problem. The lecture is also coupled with two Matlab-based labs, in order to emphasize the numerical difficulties and to provide the participant an insight of the existing tools.

Syllabus:

• Day 1: Introduction, motivating examples and model reduction problem; Overview of the approximation methods and linear algebra tools; Gramian and SVD based techniques; Moment matching and Krylov subspace based techniques.
• Day 2: Lab 1, Application of the SVD techniques and the Arnoldi procedure; H2 first order optimality conditions, generalized Krylov subspace and Tangential techniques; Advanced techniques (Mixed and Sylvester approaches / Multi-LTI and LPV problems / Tools).
• Day 3: Lab 2, Krylov based techniques and MORE Toolbox (developed within Onera by C. Poussot-Vassal).

Design Projects: analysis (15 h)

Under Floor Air Distribution for Intelligent Buildings

This new technology presents many advantages in comparison with traditional ventilation systems, such as energy consumption reduction, comfort and health. UFAD efficiency directly depends on distributed sensing capabilities (thanks to the deployment of a wireless sensor network) and on an appropriate multivariable feedback control design. The idea comes then to conceive a prototype in order to validate theoric and simulation results and to implement control algorithms. The prototype represents a ventilated floor composed of three interconnected levels: under floor, four rooms and upper floor. The related IPA projects are dedicated to air conditioning operation, with an emphasis on the modeling and control of airflow in each level and between the adjacent rooms. Controlling instability: the inverted half cube 

Unstable processes are typically not controllable with open-loop strategies and hence provide valuable benchmarks for feedback control applications. Addressing the stabilization of such processes implies a specific care of the key control design issues, such as performance limitations, communication and computation constraints, robustness, nonlinearities etc. 
The inverted half cube, designed and built by IPA students, implies to stabilize the half cube on its lower edge thanks to a cart driven with a LEGO NXT module. This novel version of the classical "inverted pendulum" implies to solve the same control problems as those associated with walking biped robots, a missile propelled by a jet reaction, a load suspended from a crane, etc...

Visit the full page about this course

Visit the full page about this course

The objective of this course is to provide a comprehensive foundation in system reliability theory and dependability analysis methods. The following topics are addressed.

• Probabilistic failure models and lifetime modelling of engineering components
• Qualitative approaches to system reliability analysis (FMECA, ...)
• Reliability modelling and analysis of systems and networks of independent components (Fault Tree Analysis, Reliability Block Diagrams, Event Tree Analysis, Structure Function, Minimal Cutsets, Importance Measures)
• Markov processes for systems and networks reliability modelling (systems with dependent components, passive redundancies, tested components, ...)
• Reliability of maintained systems and maintenance policies modelling

Visit the full page about this course

Project management (10.5 h)

The objectives of this class are to supply the bases of the project management as well as to present the good practices in industries. The quality management according to the standards ISO and the piloting by process are presented through industrial projects. 

This class contains a method to establish a CV as well as simulations of real recruitment interview.Class schedule 

Industrial seminars (27 h for IPA)

• Semi-active damper design and regulation. B. TALON, SOBEN.
• Model-based design for motor control. V. TALON, Renault.
• Case study on warm compression station for cryogenics. B. BRADU, CERN . 
• Keys and social issues to enter the industrial life. M. PRUNIER, Schneider.
• Consulting for inovation in Information Technologies. D. JACQUET, Protoptim .

Research seminars (15 h for CST)

Each year, MiSCIT and GIPSA-lab invite keynote speakers to give a short class on their research topic. The lectures (typically 15h) are given in the Control Systems Department of GIPSA-lab. They focus on the latest results in a specific topic of control and systems theory, and may include some labs to illustrate specific aspects. The attendance is composed as Master and Ph.D. students, as well as engineers, researchers and professors. A basic knowledge in dynamical systems, linear algebra and control theory is expected.

Linear Matrix Inequalities and Sum-of-Squares Optimization in Systems and Controls Theory: A Practical and Theoretical Overview (2013) 

By Mattew M. Peet, Professor of Aerospace Engineering, Arizona State University (USA)

Abstract: The topic of this course will be the use of LMI methods for optimal control of linear, nonlinear and infinite-dimensional systems. We will start by posing all major finite-dimensional optimal control problems as LMIs. This includes both output and full-state feedback control for both the H_\infty and H_2 (LQG) system norms. We will also give a brief introduction to the popular SDP solver SeDuMi. Next, we will give a background on the use of LMIs for optimization of polynomial variables such as in the Sum-of-Squares framework - including the use of the Matlab toolbox SOSTOOLS. We will discuss several theoretical tools for the optimization of polynomials such as various versions of the Positivstellensatz. Finally, we will discuss how LMIs and polynomial optimization have been use to resolve long-standing problems in analysis of nonlinear systems and systems with delay, and how these results have been extended to synthesize optimal controllers for systems with delay and certain classes of partial-differential equations.

Syllabus:

• Day 1: Convex optimization; Semidefinite programming; Linear state-space systems theory; Optimal H_2 and H_\infty dynamic output-feedback controller synthesis. 
• Day 2: Polynomial optimization, Sum-of-Squares; Polya's lemma; Ideals, Varieties; The Positivstellensatz; Robust controller synthesis 
• Day 3: Nonlinear stability analysis; Analysis and control of linear delayed systems; Analysis and control of linear partial-differential equations; Stability Analysis of nonlinear delayed and partial-differential equations. 

Model Reduction (Approximation) of Large-Scale Systems (2012) 

By Charles Poussot-Vassal, Researcher at Onera - The French Aerospace Lab.

Abstract: In the engineering area (e.g. aerospace, automotive, biology, circuits), dynamical systems are the basic framework used for modelling, controlling and analysing a large variety of systems and phenomena. Due to the increasing use of dedicated computer-based modelling design software, numerical simulation turns to be more and more used to simulate a complex system or phenomenon and shorten both development time and cost. However, the need of an enhanced model accuracy inevitably leads to an increasing number of variables and resources to manage at the price of a high numerical cost. This counterpart is the justification for model reduction (see Figure 1). 
The objective of the lecture is to introduce the model reduction (or approximation) problem, within the linear framework only, and, in an increase complexity, some of the well established and modern techniques to solve this class of problem. The lecture is also coupled with two Matlab-based labs, in order to emphasize the numerical difficulties and to provide the participant an insight of the existing tools.

Syllabus:

• Day 1: Introduction, motivating examples and model reduction problem; Overview of the approximation methods and linear algebra tools; Gramian and SVD based techniques; Moment matching and Krylov subspace based techniques.
• Day 2: Lab 1, Application of the SVD techniques and the Arnoldi procedure; H2 first order optimality conditions, generalized Krylov subspace and Tangential techniques; Advanced techniques (Mixed and Sylvester approaches / Multi-LTI and LPV problems / Tools).
• Day 3: Lab 2, Krylov based techniques and MORE Toolbox (developed within Onera by C. Poussot-Vassal).

Design Projects: analysis (15 h)

Under Floor Air Distribution for Intelligent Buildings

This new technology presents many advantages in comparison with traditional ventilation systems, such as energy consumption reduction, comfort and health. UFAD efficiency directly depends on distributed sensing capabilities (thanks to the deployment of a wireless sensor network) and on an appropriate multivariable feedback control design. The idea comes then to conceive a prototype in order to validate theoric and simulation results and to implement control algorithms. The prototype represents a ventilated floor composed of three interconnected levels: under floor, four rooms and upper floor. The related IPA projects are dedicated to air conditioning operation, with an emphasis on the modeling and control of airflow in each level and between the adjacent rooms. Controlling instability: the inverted half cube 

Unstable processes are typically not controllable with open-loop strategies and hence provide valuable benchmarks for feedback control applications. Addressing the stabilization of such processes implies a specific care of the key control design issues, such as performance limitations, communication and computation constraints, robustness, nonlinearities etc. 
The inverted half cube, designed and built by IPA students, implies to stabilize the half cube on its lower edge thanks to a cart driven with a LEGO NXT module. This novel version of the classical "inverted pendulum" implies to solve the same control problems as those associated with walking biped robots, a missile propelled by a jet reaction, a load suspended from a crane, etc...

Visit the full page about this course

Visit the full page about this course

This course is supported by the "College Doctoral" of Grenoble University. It is given in English upon request at the beginning of the session.

Summary:

Data assimilation is often presented as the art of combining various sources of information (most often, measurements and numerical models) to estimate the state of a partially observed dynamical system. In geophysics, it is now a research topic per se. It is mainly used to:
    •    define as precisely as possible a physical state (atmosphere, ocean, ...) of a system to predict its temporal evolution;
    •    optimally estimate a system state over a period of time for example, to study its variabilities;
    •    identify systematic errors in models;
    •    optimize the design of observation networks;
    •    extrapolate values of non observed variables;
    •    estimate parameters in physical laws.
The course aims at introducing the theoretical concepts and practical implementation aspects of modern data assimilation with a peculiar focus on high dimensional, non linear systems, as usually met in geosciences.

Necessary background for the course:

- Basic notions in probability and statistics (Expectation, variance, covariance matrix)
- Basic notions in linear algebra
- Basic notions in differential calculus

Program:

Part 1: Data assimilation based on estimation theory

1. Introduction to ensemble data assimilation
2. Notions in estimation theory
3. The BLUE
4. The Kalman filter
5. Ensemble Kalman filters
6. Non linear filters

Part 2: Data assimilation based on control theory

1. Introduction to variational data assimilation
2. Variational data assimilation for time-independent problems
3. The adjoint method
4. Variational Data assimilation : Practical aspect
5. Adjoint coding

Visit the full page about this course